Lp-norm regularization in volumetric imaging of cardiac current sources.

Rahimi A, Xu J, Wang L - Comput Math Methods Med (2013)

Bottom Line:
Advances in computer vision have substantially improved our ability to analyze the structure and mechanics of the heart.In a set of phantom experiments, we demonstrate the superiority of the proposed Lp-norm method over its L1 and L2 counterparts in imaging cardiac current sources with increasing extents.This ability to preserve the spatial structure of source distribution is important for revealing the potential disruption to the normal heart excitation.

ABSTRACTAdvances in computer vision have substantially improved our ability to analyze the structure and mechanics of the heart. In comparison, our ability to observe and analyze cardiac electrical activities is much limited. The progress to computationally reconstruct cardiac current sources from noninvasive voltage data sensed on the body surface has been hindered by the ill-posedness and the lack of a unique solution of the reconstruction problem. Common L2- and L1-norm regularizations tend to produce a solution that is either too diffused or too scattered to reflect the complex spatial structure of current source distribution in the heart. In this work, we propose a general regularization with Lp-norm (1 < p < 2) constraint to bridge the gap and balance between an overly smeared and overly focal solution in cardiac source reconstruction. In a set of phantom experiments, we demonstrate the superiority of the proposed Lp-norm method over its L1 and L2 counterparts in imaging cardiac current sources with increasing extents. Through computer-simulated and real-data experiments, we further demonstrate the feasibility of the proposed method in imaging the complex structure of excitation wavefront, as well as current sources distributed along the postinfarction scar border. This ability to preserve the spatial structure of source distribution is important for revealing the potential disruption to the normal heart excitation.

Mentions:
First, we consider the ability of the proposed Lp-norm regularization in reconstructing the complex structure of excitation wavefront. Figure 6(a) shows an example of an excitation wavefront during a normal propagation in a healthy ventricle at 33 ms after the onset of ventricular excitation. Similar to our earlier observations, the L1 reconstruction produces scattered solution where the spatial structure of the excitation wavefront is lost (Figure 6(b)). The L2 reconstruction, on the other extreme, produces a blurred region of activation where the structure of excitation wavefront is smeared (Figure 6(d)). In comparison, the Lp reconstruction (p = 1.5) better preserves the excitation wavefront (Figure 6(c)). Quantitatively, the Lp regularization obtains OS = 0.26, while the L1 solution provides OS = 0.07, and the L2 solution produces OS = 0.23.

Mentions:
First, we consider the ability of the proposed Lp-norm regularization in reconstructing the complex structure of excitation wavefront. Figure 6(a) shows an example of an excitation wavefront during a normal propagation in a healthy ventricle at 33 ms after the onset of ventricular excitation. Similar to our earlier observations, the L1 reconstruction produces scattered solution where the spatial structure of the excitation wavefront is lost (Figure 6(b)). The L2 reconstruction, on the other extreme, produces a blurred region of activation where the structure of excitation wavefront is smeared (Figure 6(d)). In comparison, the Lp reconstruction (p = 1.5) better preserves the excitation wavefront (Figure 6(c)). Quantitatively, the Lp regularization obtains OS = 0.26, while the L1 solution provides OS = 0.07, and the L2 solution produces OS = 0.23.

Bottom Line:
Advances in computer vision have substantially improved our ability to analyze the structure and mechanics of the heart.In a set of phantom experiments, we demonstrate the superiority of the proposed Lp-norm method over its L1 and L2 counterparts in imaging cardiac current sources with increasing extents.This ability to preserve the spatial structure of source distribution is important for revealing the potential disruption to the normal heart excitation.

ABSTRACTAdvances in computer vision have substantially improved our ability to analyze the structure and mechanics of the heart. In comparison, our ability to observe and analyze cardiac electrical activities is much limited. The progress to computationally reconstruct cardiac current sources from noninvasive voltage data sensed on the body surface has been hindered by the ill-posedness and the lack of a unique solution of the reconstruction problem. Common L2- and L1-norm regularizations tend to produce a solution that is either too diffused or too scattered to reflect the complex spatial structure of current source distribution in the heart. In this work, we propose a general regularization with Lp-norm (1 < p < 2) constraint to bridge the gap and balance between an overly smeared and overly focal solution in cardiac source reconstruction. In a set of phantom experiments, we demonstrate the superiority of the proposed Lp-norm method over its L1 and L2 counterparts in imaging cardiac current sources with increasing extents. Through computer-simulated and real-data experiments, we further demonstrate the feasibility of the proposed method in imaging the complex structure of excitation wavefront, as well as current sources distributed along the postinfarction scar border. This ability to preserve the spatial structure of source distribution is important for revealing the potential disruption to the normal heart excitation.